Original paper
Abstract
Positive option-implied risk-neutral skewness (RNS) predicts next-month abnormal underlying stock returns driven by upward rebounds of previously undervalued stocks. The RNS anomaly is strongest in periods of post-recession rebounds when momentum crashes occur. Furthermore, the momentum anomaly is strongest (weakest) in stocks with the most negative (positive) RNS. We generalize our findings to non-optionable stocks by constructing an RNS factor-mimicking portfolio, finding that a momentum strategy that avoids performance reversals has meaningfully superior performance. Our results hold after controlling for trading frictions, firm characteristics, and common risk factors.
Keywords:Â Risk Neutral Skewness, Momentum, Return Predictability
Trading rules
- Selection criteria: Stocks from NYSE/AMEX/NASDAQ valued over $5 and having a market cap higher than 50% of the NYSE.
- Measure of skewness: Highest daily gain during the previous month.
- Monthly sorting method:
- Organize stocks into five groups based on projected skewness (peak daily gain).
- Within those groups, sort stocks further into quintiles depending on their cumulative returns from the last year.
- Defining momentum: Use a year-long formation duration, hold for a month, and skip for one month.
- Procedure for monthly portfolio setup:
- For long positions: Pick from the winners with the strongest negative skew.
- For short positions: Pick from the losers with the most significant positive skew.
- Equally weighted.
- Rebalanced monthly.
Python code
Backtrader
Here is the Backtrader python code for the given trading rules:
import backtrader as bt
import pandas as pd
import numpy as np
class SkewMomentumStrategy(bt.Strategy):
params = (
('formation_period', 12),
('holding_period', 1),
('skip_period', 1),
('min_price', 5),
('capitalization_percentile', 0.5),
)
def __init__(self):
self.inds = {}
for d in self.datas:
self.inds[d] = {}
self.inds[d]['max_return'] = bt.indicators.Highest(d.close(-1) / d.close(-2), period=21)
self.inds[d]['momentum'] = d.close / d.close(-self.p.formation_period) - 1
def prenext(self):
self.next()
def next(self):
if self._count % (self.p.holding_period + self.p.skip_period) != 0:
return
stocks = self.datas
stocks = [d for d in stocks if d.close[0] > self.p.min_price]
market_caps = np.array([d.market_cap[0] for d in stocks])
threshold = np.percentile(market_caps, self.p.capitalization_percentile * 100)
stocks = [d for d, mc in zip(stocks, market_caps) if mc >= threshold]
skews = np.array([self.inds[d]['max_return'][0] for d in stocks])
momentum = np.array([self.inds[d]['momentum'][0] for d in stocks])
skew_quintiles = pd.qcut(skews, 5, labels=False)
momentum_quintiles = pd.qcut(momentum, 5, labels=False)
long_candidates = [d for d, sq, mq in zip(stocks, skew_quintiles, momentum_quintiles) if sq == 0 and mq == 4]
short_candidates = [d for d, sq, mq in zip(stocks, skew_quintiles, momentum_quintiles) if sq == 4 and mq == 0]
long_weight = 1.0 / len(long_candidates) if long_candidates else 0
short_weight = -1.0 / len(short_candidates) if short_candidates else 0
for d in long_candidates:
self.order_target_percent(d, target=long_weight)
for d in short_candidates:
self.order_target_percent(d, target=short_weight)
for d in set(self.datas) - set(long_candidates + short_candidates):
self.order_target_percent(d, target=0)This code defines a SkewMomentumStrategy class that implements the trading rules. The strategy calculates skewness proxies and past momentum for each stock, sorts them into quintiles, and constructs a long-short portfolio according to the specified criteria. The positions are equally weighted and rebalanced monthly.